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Republicans, whose numbers on Beacon Hill have dwindled to the lowest level in years, are hoping that voter dissatisfaction will carry a new crop of candidates to victory in next week’s legislative elections.

“We have the benefit of voter disgust with Beacon Hill,’’ said Jennifer Nassour, state Republican Party chairwoman. “People are really tired of paying higher taxes that fund waste, patronage, and corruption.’’

Democrats, meanwhile, are predicting they will retain their overwhelming majority in the Legislature and possibly add to it by winning open seats that were previously held by Republicans. And they are targeting a handful of the 20 incumbent Republicans, the ones Democrats believe are especially vulnerable.

“The Massachusetts Democratic Party has fielded a larger group of candidates, more experienced candidates, and more qualified candidates than the Republicans,’’ asserted state Dem ocratic Party chairman John Walsh.

More long-time incumbents are facing challengers than in previous years, Walsh said. Republicans are running in 95 of the 111 contested legislative races.

Even Senate President Therese Murray, who has not had an opponent since 2004, is campaigning hard. Her district, which stretches from Pembroke to the Upper Cape, is among the most conservative in the state, and her Republican opponent, Thomas F. Keyes, is hoping to capitalize on voter unease.

“Politics is all about timing,’’ he told a Globe reporter recently. “Right now, I have the message that people are looking for.’’

Murray counters that she is in tune with her fiscally conservative district.

Six Republicans — Senator Richard Tisei and Representatives Karyn Polito, Lewis Evangelidis, Jeffrey Perry, Richard Ross, and Robert Hargraves — are retiring or running for higher office. Many sitting lawmakers in both parties are leaving Beacon Hill after this year.

Running to succeed Tisei, who is the Republican candidate for lieutenant governor, are state Representative Katherine Clark, Democrat of Melrose, and city councilor Craig Spadafora of Malden, a Republican. Spadafora’s campaign drew some unwanted attention when comic Lenny Clarke, appearing at a fund-raiser for him, called Clark a “whore.’’ Spadafora won the Globe’s endorsement.

Running for Clark’s seat are Melrose alderman Paul Brodeur, a Democrat and lawyer who works for the state, and Republican David Lucas, also a lawyer and former Melrose city solicitor.

Many Democratic incumbents, including Senator Susan Fargo of Lincoln and Representative Allen McCarthy of East Bridgewater, who are locked in tough battles with conservative challengers, have been sounding traditionally Republican themes such as lower taxes and spending cuts.

Fargo, a seven-term senator from Lincoln, is being challenged by Sandi Martinez, a three-time Republican candidate from Chelmsford who helped found the Greater Lowell Tea Party.

McCarthy is facing Geoff Diehl, a Whitman Finance Committee member and sign company account executive. The candidates have battled over taxes and immigration. McCarthy, who acknowledges that he is in a tough battle, has been getting fund-raising and other help from House Speaker Robert A. DeLeo, according to members of DeLeo’s leadership team.

In this volatile year, Democrats, too, are eyeing seats held by incumbents. They hope, for example, to unseat state Representative Daniel Webster of Pembroke, who is facing Josh Cutler of Duxbury. Cutler was editor of the Duxbury Clipper newspaper until he stepped down to run.

But Democrats also fear that the congressional race between Perry, a Republican from Sandwich, and Norfolk District Attorney William R. Keating could cost them seats on the South Shore.

“We’re watching the 35 races from Quincy south,’’ said Representative Patricia Haddad, who is coordinating the campaign effort for DeLeo. “There is a potential Perry effect. They will pull out a totally different demographic than we’ve seen in the past.’’

State Representative Matthew Patrick of Falmouth, a liberal Democrat, could be one of the casualties. He is facing a tough challenge from Republican David Vieira of Falmouth, who was endorsed this week by the Cape Cod Times. Vieira, an official of the Barnstable County sheriff’s office, has served as Town Meeting moderator. Patrick has been an outspoken critic of legislative leadership on Beacon Hill, challenging a resistant DeLeo to detail hundreds of thousands of dollars in legal bills the House paid in connection with the federal investigation of former House speaker Salvatore DiMasi.

Other incumbents are also facing aggressive challengers. Nine-term representative James Fagan of Taunton is embroiled in a fierce campaign with Republican Shaunna O’Connell, also of Taunton. O’Connell recently distributed literature that came with a 20-second audio clip of Fagan railing on the House floor against a bill to increase minimum mandatory sentences for sex offenders.

Fagan, a defense lawyer, argued during debate that if the bill passed, criminals would agree to plea bargains less often and more cases would go to trial. That would traumatize victims, he said. As a defense lawyer, he would then have to “rip them apart,’’ he said.

O’Connell has also accused Fagan of belittling her. At one debate, he suggested she wouldn’t be able to answer a particular question because, he said, “you have to count.’’